This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A225168 #5 May 01 2013 12:24:20 %S A225168 1,8,584,3490568,138073441864904,236788599971507074896206759048, %T A225168 756988343475413525492604622110601759725560263205883476698184 %N A225168 Denominators of the sequence s(n) of the sum resp. product of fractions f(n) defined recursively by f(1) = 9/1; f(n+1) is chosen so that the sum and the product of the first n terms of the sequence are equal. %C A225168 Numerators of the sequence s(n) of the sum resp. product of fractions f(n) is A165427(n+2), hence sum(A165427(i+1)/A225161(i),i=1..n) = product(A165427(i+1)/A225161(i),i=1..n) = A165427(n+2)/a(n) = A165421(n+3)/a(n) = A011764(n)/a(n). %F A225168 a(n) = 9^(2^(n-1))*b(n) where b(n)=b(n-1)-b(n-1)^2 with b(1)=1/9. %e A225168 f(n) = 9, 9/8, 81/73, 6561/5977, ... %e A225168 9 + 9/8 = 9 * 9/8 = 81/8; 9 + 9/8 + 81/73 = 9 * 9/8 * 81/73 = 6561/584; ... %e A225168 s(n) = 1/b(n) = 9, 81/8, 6561/584, ... %p A225168 b:=proc(n) option remember; b(n-1)-b(n-1)^2; end: %p A225168 b(1):=1/9; %p A225168 a:=n->9^(2^(n-1))*b(n); %p A225168 seq(a(i),i=1..8); %Y A225168 Cf. A011764, A076628, A165421, A165427, A225161. %K A225168 nonn %O A225168 1,2 %A A225168 _Martin Renner_, Apr 30 2013